Theory of contact for geometric continuity of parametric curves |
| |
Authors: | Chih Lee Bahram Ravani An Tzu Yang |
| |
Affiliation: | (1) Computer Integrated Design and Manufacturing Laboratory, Department of Mechanical, Aeronautical and Materials Engineering, University of California-Davis, 95616 Davis, CA, USA |
| |
Abstract: | This paper develops a theory of contact for piecewise parametric curves based on the differential geometry of evolutes, polar curves, and binormal indicatrices. This theory is completely geometric, independent of parametrization and generalizes to any order. Two sets of dimensionless, characteristic numbers describing the local geometry of a curve up tonth order are defined. These characteristic numbers can be used to describe conditions for higher order contacts in an algebraic fashion. The same characteristic numbers can also be used to interpret contact conditions of up tonth order in terms of the geometry of higher evolutes and binormal indicatrices. The resulting geometric contact conditions are used to design piecewise parametric curves for Computer Aided Geometric Design (CAGD) applications. |
| |
Keywords: | Geometric continuity Geometric contact Evolutes Polar curves Binormal indicatrices |
本文献已被 SpringerLink 等数据库收录! |
|